In mathematics, Lévy's modulus of continuity theorem gives a result about the almost sure behaviour of an estimate of the modulus of continuity for the Wiener process, which models Brownian motion. It is due to the French mathematician Paul Lévy.
Statement of the result
Let
In other words, the sample paths of Brownian motion have modulus of continuity
with probability one, and for sufficiently small
References
Lévy's modulus of continuity theorem Wikipedia(Text) CC BY-SA